Finite Group Databasebeta

← #11870463

Subgroups — #11870463

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 829 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594605C211yesmaximal, characteristic, complemented
2#10594518C211yesmaximal, characteristic, complemented
3#10592581C211yesmaximal, characteristic, complemented
4C3×#4890C211yesmaximal, characteristic, complemented
5C3×#4872C211yesmaximal, characteristic, complemented
6#10590945C211yesmaximal, characteristic, complemented
7#10590753C211yesmaximal, characteristic, complemented
8#10590745C211yesmaximal, characteristic, complemented
9#10590643C211yesmaximal, characteristic, complemented
10#10590598C211yesmaximal, characteristic, complemented
11#10590547C211yesmaximal, characteristic, complemented
12#10590510C211yesmaximal, characteristic, complemented
13#10590463C211yesmaximal, characteristic, complemented
14#10590456C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#80948—31nomaximal
17#79590—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×C4×D32—21no—
20C2×#3799—21no—
21#64104C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C2×C3×D24C2211yescharacteristic
24C3×#893C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#893C2211yescharacteristic, complemented
27C3×#888C2211yescharacteristic, complemented
28#63921—21no—
29#63916C2211yescharacteristic
30#63911C2211yescharacteristic, complemented
31#63910—21no—
32#63907—21no—
33#63904—21no—
34#63894C2211yescharacteristic, complemented
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37C4×#624C2211yescharacteristic
38#63879—21no—
39#63879—21no—
40C2×#3714C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C32×#107C2211yescharacteristic, complemented
44#63648C2211yescharacteristic, complemented
45#63647C2211yescharacteristic
46#63636C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic, complemented
50C3×C8×Dic3C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54C3×#807C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5725—31no—
62#5548—31no—
63C4×D3×D4—31no—
64C4×D3×D4—31no—
65C3×#474—31no—
66C3×C4×D8—31no—
67#5156—31no—
68#5150—31no—
69#5087—31no—
70#5015—31no—
71C4×#213—31no—
72C4×#213—31no—
73#4890D311yescharacteristic, complemented
74#4882—31no—
75#4882—31no—
76#4882—31no—
77#4882—61no—
78#4872—31no—
79#4872D311yescharacteristic, complemented
80#4843—31no—
81#4833—31no—
82#4786—31no—
83#4774—31no—
84#4773—31no—
85#4773—31no—
86#4773—31no—
87#4759—31no—
88#4756—31no—
89#4756—31no—
90C4×D24—31no—
91#4685—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×Dic6—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×#624—21no—
109C2×#624D411yescharacteristic
110C2×#624D411yescharacteristic
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113#3802—22no—
114#3802—22no—
115C4×D32—44no—
116#3799—44no—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119C32×C4⋊C4C2311yescharacteristic
120#3752—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×D24—22no—
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32D411yescharacteristic
139Dic32D411yescharacteristic
140#3714—22no—
141#3714—22no—
142#3713—22no—
143#3100—91noSylow
144C2×#239—61no—
145C2×D3×D4—31no—
146C2×D3×D4—31no—
147C2×#235—61no—
148C22×C4×D3—61no—
149C22×C4×D3—61no—
150C2×C3×D8—31no—
151C3×C4⋊Q8—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155#947—61no—
156#940—31no—
157#938—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160C2×#213—31no—
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—31no—
164C4×#67—61no—
165C4×#67—61no—
166C4×#67—61no—
167C2×D24—31no—
168C2×D24—31no—
169C2×D24C2×D311yescharacteristic
170#895—31no—
171#895—31no—
172#895—31no—
173#895—61no—
174#895—61no—
175#893—31no—
176#893—61no—
177#893C2×D311yescharacteristic
178#893C2×D311yescharacteristic
179#893C2×D311yescharacteristic, complemented
180D3×C4⋊C4—31no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—61no—
183#888C2×D311yescharacteristic, complemented
184#885—61no—
185#884—61no—
186#67⋊C4—61no—
187#67⋊C4—61no—
188D3×C22⋊C4—61no—
189D3×C22⋊C4—61no—
190#874—31no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—31no—
194C42×D3—31no—
195C42×D3—31no—
196C3×#107—21no—
197C3×#107—31no—
198C3×#107C2×D311yescharacteristic, complemented
199C3×#107C2×D311yescharacteristic, complemented
200C3×C4⋊C8—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×C4×C8—31no—
206#832—31no—
207#832—31no—
208#821—31no—
209#821—31no—
210#821—31no—
211#821—61no—
212#821C2×D311yescharacteristic
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—61no—
218#818—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8C2×D311yescharacteristic, complemented
221C8×Dic3—31no—
222C8×Dic3C2×D311yescharacteristic, complemented
223#809—31no—
224#809—31no—
225#809—31no—
226#809—61no—
227#809C2×D311yescharacteristic
228#809C2×D311yescharacteristic
229#809C2×D311yescharacteristic, complemented
230#807—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234#807C2×D311yescharacteristic, complemented
235C4⋊(C3⋊C8)—31no—
236C4×C3⋊C8—31no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C2×D32—24no—
243C2×D32—42no—
244C2×D32—42no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—42no—
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C4×C3⋊D3—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12#4112yescomplemented
266C3×D12#4112yescomplemented
267C3×C4×D3—42no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×Dic6—42no—
271#626—42no—
272#626—42no—
273#626—42no—
274#625—24no—
275#624—41no—
276#624—42no—
277#624D814yescomplemented
278D3×Dic3—42no—
279D3×Dic3—42no—
280C32×C8—21no—
281C3⋊(C3⋊C8)—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284#532—91no—
285C2×C4×D4—91no—
286#480—91no—
287#480—91no—
288#474—31no—
289#474—91no—
290#459—91no—
291#459—91no—
292#447—91no—
293#447—91no—
294C4×D8—31no—
295C4×D8—91no—
296C4×D8—91no—
297C4×D8—91no—
298#431—91no—
299C23×D3—61no—
300C23×D3—61no—
301C2×C3×Q8—61no—
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315#239—124no—
316D3×D4—62no—
317D3×D4—62no—
318D3×D4—62no—
319D3×D4—62no—
320#235—124no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—121no—
330C2×D12C22×D311yescharacteristic
331C2×D12C22×D311yescharacteristic
332C2×D12C22×D311yescharacteristic
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3—31no—
337C2×C4×D3—31no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—121no—
350C2×C4×D3—124no—
351C2×C4×D3—124no—
352C2×Dic6—21no—
353C3×D8—62no—
354C2×C3×C8—21no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C42—31no—
371C3×C42—31no—
372#217—61no—
373#217—61no—
374#217—61no—
375#213—62no—
376#213—62no—
377#213—62no—
378#213—62no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—121no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3C22×D311yescharacteristic
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409D24—22no—
410D24—62no—
411D24—62no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3C2×D812yes—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428D32—48no—
429C32×C4—41no—
430C32×C4—41no—
431C32×C4C2×#4111yescharacteristic
432C32×C4C2×#4111yescharacteristic
433C3⋊Dic3—21no—
434C3⋊Dic3—41no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3C2×D812yes—
439C3×Dic3C2×D812yes—
440C2×#41—181no—
441C22×D4—91no—
442C23×C4—181no—
443C2×D8—31no—
444C2×D8—91no—
445C2×D8—91no—
446C2×D8—91no—
447C4⋊Q8—31no—
448#127—91no—
449#124—181no—
450#121—91no—
451#121—91no—
452#121—181no—
453C4×D4—31no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460C4×D4—181no—
461C4×D4—181no—
462C2×C4⋊C4—91no—
463C2×C22⋊C4—181no—
464C2×C42—91no—
465#107—31no—
466#107—91no—
467#107—91no—
468#107D3211yescharacteristic, complemented
469C4⋊C8—31no—
470C4⋊C8—91no—
471#102—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—91no—
480C22⋊C8—91no—
481C4×C8—31no—
482C4×C8—91no—
483C23×C3—61no—
484C23×C3—61no—
485C23×C3—61no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—31no—
490C22×D3—31no—
491C22×D3—61no—
492C22×D3—64no—
493C22×D3—64no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—121no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C3×Q8—122no—
502C3×D4—32no—
503C3×D4—32no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—61no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—122no—
521C2×C3×C4—122no—
522C2×C3×C4—122no—
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525#67—64no—
526#67—64no—
527#67—122no—
528#67—122no—
529#67—122no—
530C2×Dic3—21no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—121no—
537C2×Dic3—122no—
538C2×Dic3—122no—
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543D12—21no—
544D12—21no—
545D12—21no—
546D12—21no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—121no—
552D12—121no—
553D12—122no—
554D12—122no—
555D12—122no—
556D12—122no—
557D12—122no—
558D12—242no—
559D12#23512yescomplemented
560D12#23912yescomplemented
561C4×D3—34no—
562C4×D3—34no—
563C4×D3—42no—
564C4×D3—42no—
565C4×D3—42no—
566C4×D3—61no—
567C4×D3—61no—
568C4×D3—61no—
569C4×D3—61no—
570C4×D3—121no—
571C4×D3—121no—
572C4×D3—121no—
573C4×D3—121no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—122no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—242no—
581Dic6—42no—
582C3×C8—21no—
583C3×C8—21no—
584C3×C8—41no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C3⋊C8—61no—
590C3⋊C8—61no—
591C3⋊C8—121no—
592C2×C32#52511yescharacteristic
593C2×C32C22×D811yescharacteristic
594C2×C32#57511yescharacteristic
595C3⋊D3—22no—
596C3⋊D3—81no—
597C3×D3—42no—
598C3×D3—42no—
599C3×D3—81no—
600C24—181no—
601#41—364no—
602C2×Q8—61no—
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—91no—
607C2×D4—181no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4—181no—
612C2×D4—182no—
613C2×D4—182no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—91no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4—364no—
625D8—62no—
626D8—182no—
627D8—182no—
628D8—182no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—91no—
632C2×C8C2×D3211yescharacteristic
633C4⋊C4—31no—
634C4⋊C4—61no—
635C4⋊C4—91no—
636C4⋊C4—181no—
637C4⋊C4C2×D3211yescharacteristic
638C4⋊C4C2×D3211yescharacteristic
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C42—31no—
648C42—31no—
649C42—91no—
650C42—91no—
651C22×C3—21no—
652C22×C3—62no—
653C22×C3—62no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C2×D3×D411yescharacteristic
663C2×D3—22no—
664C2×D3—22no—
665C2×D3—32no—
666C2×D3—32no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—62no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—128no—
682C2×D3—128no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—241no—
690C2×D3—241no—
691C2×D3—241no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—32no—
695C3×C4—32no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—81no—
703C3×C4—81no—
704C3×C4—121no—
705C3×C4C2×#23511yescharacteristic
706C3×C4C2×#23911yescharacteristic
707C3×C4D3×#4111yescharacteristic
708C3×C4D3×#4111yescharacteristic
709Dic3—21no—
710Dic3—21no—
711Dic3—41no—
712Dic3—61no—
713Dic3—61no—
714Dic3—121no—
715Dic3—121no—
716Dic3—121no—
717Dic3—241no—
718Dic3D3×D812yes—
719Dic3D3×D812yes—
720C32#310011yescharacteristic, complemented, Sylow
721C23—61no—
722C23—61no—
723C23—61no—
724C23—91no—
725C23—184no—
726C23—181no—
727C23—362no—
728C23—362no—
729Q8—122no—
730D4—32no—
731D4—32no—
732D4—61no—
733D4—61no—
734D4—61no—
735D4—61no—
736D4—184no—
737D4—181no—
738D4—181no—
739D4—362no—
740D4—362no—
741D4—362no—
742D4—362no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—31no—
749C2×C4—61no—
750C2×C4—94no—
751C2×C4—91no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—122no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—181no—
758C2×C4—362no—
759C2×C4—362no—
760C2×C4—362no—
761C2×C4—362no—
762C2×C4—361no—
763C2×C4C22×D3211yescharacteristic
764C8—21no—
765C8—61no—
766C8—61no—
767C8—181no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—122no—
772C2×C3—122no—
773C2×C3—241no—
774C2×C3#554711yescharacteristic
775C2×C3#562711yescharacteristic
776C2×C3C2×D3×D811yescharacteristic
777C2×C3C2×D3×D811yescharacteristic
778C2×C3#576811yescharacteristic
779C2×C3#577711yescharacteristic
780D3—42no—
781D3—42no—
782D3—62no—
783D3—62no—
784D3—81no—
785D3—122no—
786D3—241no—
787D3—241no—
788D3—481no—
789C22—62no—
790C22—62no—
791C22—92no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—181no—
800C22—181no—
801C22—368no—
802C22—361no—
803C22—361no—
804C22—361no—
805C22D32×D411yescharacteristic
806C4—32no—
807C4—32no—
808C4—41no—
809C4—41no—
810C4—61no—
811C4—61no—
812C4—121no—
813C4—181no—
814C4—361no—
815C4D3×#23511yescharacteristic
816C4D3×#23911yescharacteristic
817C3—21no—
818C3#7959011yescharacteristic, complemented
819C3#8094811yescharacteristic, complemented
820C2—122no—
821C2—122no—
822C2—182no—
823C2—241no—
824C2—721no—
825C2#1059462311yescharacteristic
826C2D32×D811yescharacteristic
827C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10594605C2semidirect
2. #10594518C2semidirect
3. #10592581C2semidirect
4. C3×#4890C2semidirect
5. C3×#4872C2semidirect
6. #10590945C2semidirect
7. #10590753C2semidirect
8. #10590745C2semidirect
9. #10590643C2semidirect
10. #10590598C2semidirect
11. #10590547C2semidirect
12. #10590510C2semidirect
13. #10590463C2semidirect
14. #10590456C2semidirect
15. #10590452C2semidirect
26. C3×#893C22semidirect
27. C3×#888C22semidirect
30. #63911C22semidirect
34. #63894C22semidirect
43. C32×#107C22semidirect
44. #63648C22semidirect
46. #63636C22semidirect
47. #63634C22semidirect
49. C3×Dic3⋊C8C22semidirect
50. C3×C8×Dic3C22semidirect
53. C3×#809C22semidirect
54. C3×#807C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63563C22semidirect
60. Dic3×C3⋊C8C22semidirect
73. #4890D3semidirect
79. #4872D3semidirect
179. #893C2×D3semidirect
183. #888C2×D3semidirect
198. C3×#107C2×D3semidirect
199. C3×#107C2×D3semidirect
220. Dic3⋊C8C2×D3semidirect
222. C8×Dic3C2×D3semidirect
229. #809C2×D3semidirect
234. #807C2×D3semidirect
265. C3×D12#41semidirect
266. C3×D12#41semidirect
277. #624D8semidirect
468. #107D32semidirect
559. D12#235semidirect
560. D12#239semidirect
720. C32#3100semidirect
818. C3#79590semidirect
819. C3#80948semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105946052
#105945182
#105925812
C3×#48902
C3×#48722
#105909452
#105907532
#105907452
#105906432
#105905982
#105905472
#105905102
#105904632
#105904562
#105904522
#809483
#795903